Ama-Quartiles Edatha Yeqembu
I-Pendahuluan
Izibalo, igatsha lesayensi elibhekene nokuqoqwa, ukuhlaziywa, ukuchazwa, ukwethula, kanye nokuhlela idatha, linemiqondo eminingi ebalulekile esiza ekwenzeni izinqumo eziqhutshwa idatha. Umqondo owodwa obalulekile wezibalo ekuhlaziyweni kwedatha ama-quartiles. Ama-quartiles asiza ukuqonda ukusatshalaliswa kwedatha nokuthi idatha ihlelwa kanjani ngamaqoqo. Kulesi sihloko, sizoxoxa ngama-quartiles ngokuningiliziwe kumongo wedatha eqoqwe ngamaqoqo, ukuthi ungawabala kanjani, nokuthi ukuhumusha imiphumela kunganikeza kanjani ukuqonda okujulile ngokusatshalaliswa kwedatha.
Ukuqonda Ama-Quartiles
Kalula nje, ama-quartile ayinani elihlukanisa idatha ibe yizingxenye ezine ezilinganayo. Kumongo wokusatshalaliswa kwedatha, ama-quartile ahlukanisa idatha ibe amaphuzu amathathu, akha izikhawu ezine. La maphuzu amathathu: i-First Quartile (Q1), i-Second Quartile (Q2), kanye ne-Third Quartile (Q3) ayisisekelo ekuhlaziyweni kwezibalo. I-quartile ngayinye inencazelo nomsebenzi ohlukile ekuqondeni idatha.
– Ikota Yokuqala (Q1): Leli inani eliphakathi lengxenye engezansi yedatha, eyaziwa nangokuthi i-25th percentile.
– I-Second Quartile (Q2): Leli inani eliphakathi layo yonke idatha, eyaziwa nangokuthi i-median noma i-50th percentile.
– Ikota Yesithathu (Q3): Leli inani eliphakathi lengxenye ephezulu yedatha, eyaziwa nangokuthi i-75th percentile.
Ama-Quartile asetshenziselwa ukuchaza izici ezahlukahlukene zokusatshalaliswa futhi anikeze ulwazi oluningiliziwe mayelana nobubanzi kanye nokuvumelana kwedatha.
Ama-Quartile kudatha eqoqwe
Ezweni langempela, idatha eqoqwe ngokuvamile ayiqoqwanga (idatha eluhlaza) kodwa iqoqwa ngamaqembu anemvamisa yawo (idatha eqoqwe). Ukuhlaziya idatha eqoqwe kuhloswe ukunikeza ulwazi mayelana nendlela idatha esakazwa ngayo ezigabeni noma ezigabeni ezahlukene. Ukubala ama-quartiles edatha eqoqwe kuhilela izinyathelo eziningana ezahlukene kunedatha engaqoqwanga.
Izinyathelo Zokubala Ama-Quartile Edatha Eqoqwe
Ukuze sibale ama-quartile kudatha eqoqwe ngamaqoqo, sidinga ulwazi oluyisisekelo oluvela ekusabalalisweni kwemvamisa, njengemikhawulo yekilasi ephezulu nephansi, imvamisa yekilasi ngalinye, kanye nemvamisa eqoqwe. Nazi izinyathelo zokubala ama-quartile edatha eqoqwe ngamaqoqo:
1. Nquma iKlasi le-Quartile:
– I-First Quartile (Q1): Itholakala ezifundweni lapho imvamisa ehlanganisiwe isondela khona \( \frac{N}{4} \)
– I-Second Quartile (Q2) noma i-Median: Itholakala ezigabeni lapho imvamisa ehlanganisiwe isondela khona ku-\( \frac{N}{2} \)
– I-Third Quartile (Q3): Itholakala ezigabeni lapho imvamisa ehlanganisiwe isondela khona \( \frac{3N}{4} \)
2. Sebenzisa i-Quartile Formula yeDatha Eqoqwe Ngokuhlangana:
– Ifomula ye-First Quartile (Q1):
\[
Q1 = L + \left( \frac{\frac{N}{4} – Fk}{f} \right) \times c
\]
– Ifomula ye-Second Quartile (Q2):
\[
Q2 = L + \left( \frac{\frac{N}{2} – Fk}{f} \right) \times c
\]
– Ifomula ye-Third Quartile (Q3):
\[
Q3 = L + \kwesobunxele( \frac{\frac{3N}{4} – Fk}{f} \kwesokudla) \izikhathi c
\]
Di mana:
– \( L \) umkhawulo ophansi wekilasi lama-quartile
– \( N \) imvamisa iyonke
– \( Fk \) imvamisa ehlanganisiwe kuze kufike ekilasini lekota
– \( f \) imvamisa yekilasi lekota
– \( c \) ububanzi beklasi
Isibonelo Sokubalwa Kwekota Kwedatha Eqoqwe Ngamaqoqo
Ukuze kube lula ukuqonda, ake sibheke isibonelo esilandelayo:
Ukusatshalaliswa kwemvamisa yedatha kungokulandelayo:
| Isikhawu Sekilasi | Imvamisa (f) |
|——————-|——————|
| 10 – 20 | 5 |
| 20 – 30 | 8 |
| 30 – 40 | 12 |
| 40 – 50 | 7 |
| 50 – 60 | 3 |
I-Langkah-langkah:
1. Thola u-N: Imvamisa iyonke \( N = 5 + 8 + 12 + 7 + 3 = 35 \)
2. Imvamisa Ehlanganisiwe (Fk):
| Isigaba Sesikhawu | Imvamisa (f) | Imvamisa Ehlanganisiwe (Fk) |
|——————-|——————|———————–|
| 10 – 20 | 5 | 5 |
| 20 – 30 | 8 | 13 |
| 30 – 40 | 12 | 25 |
| 40 – 50 | 7 | 32 |
| 50 – 60 | 3 | 35 |
3. Ukuthola Amakilasi E-Quartile:
– Q1: \( \frac{N}{4} = 8.75 \) usekilasini 20 – 30
– Q2: \( \frac{N}{2} = 17.5 \) usekilasini 30 – 40
– Umbuzo 3: \( \frac{3N}{4} = 26.25 \) usekilasini 40 – 50
4. Ukubala ama-Quartiles:
– Ku-Q1:
– \( L = 20 \)
– \( Fk = 5 \)
– \( f = 8 \)
– \( c = 10 \)
\[
Q1 = 20 + \kwesobunxele( \frac{8.75 – 5}{8} \kwesokudla) \izikhathi 10 = 20 + (0.46875) \izikhathi 10 = 24.6875
\]
– Ku-Q2:
– \( L = 30 \)
– \( Fk = 13 \)
– \( f = 12 \)
– \( c = 10 \)
\[
Q2 = 30 + \kwesobunxele( \frac{17.5 – 13}{12} \kwesokudla) \izikhathi 10 = 30 + (0.375) \izikhathi 10 = 33.75
\]
– Ku-Q3:
– \( L = 40 \)
– \( Fk = 25 \)
– \( f = 7 \)
– \( c = 10 \)
\[
Q3 = 40 + \kwesobunxele( \frac{26.25 – 25}{7} \kwesokudla) \izikhathi 10 = 40 + (0.17857) \izikhathi 10 = 41.7857
\]
Ukuhunyushwa Kwemiphumela
Sisebenzisa izibalo ezingenhla, sithola ukuthi:
– Q1 = 24.6875
– Q2 = 33.75
– Q3 = 41.7857
Lezi zingxenye ezintathu zisinika ulwazi olwengeziwe mayelana nokusatshalaliswa kwedatha:
– Q1=24.6875: 25% yedatha ingaphansi kuka-24.6875
– Q2=33.75: 50% yedatha ingaphansi kuka-33.75
– Q3=41.7857: 75% yedatha ingaphansi kuka-41.7857
Ulwazi lwe-Quartile lusenza siqonde ukuqoqwa kwedatha kanye nobubanzi bayo bokuhlukahluka. Lolu lwazi lungaba usizo kakhulu ekwenzeni izinqumo kanye nokuhlaziywa kwedatha okwengeziwe, njengokutholwa kwangaphandle noma ukuhlolwa kokusebenza kwesistimu.
Isiphetho
Ama-Quartile kudatha eqoqwe ngamaqoqo adlala indima ebalulekile ekuhlaziyweni kwezibalo. Ngezindlela ezifanele, singaqonda ukusatshalaliswa kwedatha ngemininingwane eminingi nangokunemba okukhulu. Lolu lwazi alugcini nje ngokusiza ekuchazeni idatha kodwa futhi lusiza ekwenzeni izinqumo ezinolwazi oluthe xaxa ngokusekelwe ebufakazini obubonakalayo. Ekuphetheni, ukuqonda ukuthi ungabala kanjani futhi uhumushe kanjani ama-quartile kudatha eqoqwe ngamaqoqo kuyikhono eliyisisekelo wonke umhlaziyi wedatha okumele alifunde.
